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    <title>Real and Complex Root Computation package</title>
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    <h1>Real and Complex Root Computation package.</h1>

<p>
  This package contains classes for the computation of 
  isolating and refining intervals of real roots and complex roots of univariate polynomials.
</p>
<p>
  For the computation of real roots the main interface is <code>RealRoots</code> 
  and main implementing class is <code>RealRootsSturm</code>.
  The implementation follows in part 
  section 8.8 "Computation of real zeroes of Polynomial Systems" 
  in <em>Gr&ouml;bner Bases</em>, A computational Approach to Commutative Algebra, by Becker et al.
  <br />
  The class <code>RealAlgebraicNumber</code> is based on <code>AlgebraicNumber</code> 
  with factory class <code>RealAlgebraicRing</code> based on <code>AlgebraicNumberRing</code>.
  They implement real algebraic numbers, which are algebraic numbers plus an  
  isolating interval for a real root of the generator.
  <code>RealRootsSturm</code> can be applied to polynomials with real algebraic numbers.
</p>
<p>
  For the computation of complex roots the main interface is <code>ComplexRoots</code> 
  and the main implementing class is <code>ComplexRootsSturm</code>.
  The implementation provides an exact infallible method which follows the numeric method of Wilf 
  (see Wilf: A global bisection algorithm for computing the zeros of polynomials in the complex plane).
  It uses Sturm sequences following the Routh-Hurwitz Method 
  to count the number of complex roots within a rectangle in the complex plane.  
  For a (eventually) more efficient method see: 
  Collins and Krandick: An efficient algorithm for infallible polynomial complex root isolation,
  in ISSAC'92.
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    <hr />
    <address><a href="mailto:kredel at rz.uni-mannheim.de">Heinz Kredel</a></address>
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<!-- Created: Sat Mar 21 20:20:15 CET 2009 -->
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Last modified: Sun Dec 20 22:33:25 CET 2009
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